HarrodandtheCambridgeKeynesians
FionaMaclachlan
DepartmentofEconomicsandFinance
ManhattanCollege,Riverdale,NY10471
[email protected]
________________________________________________________________________________
Abstract
HarrodandthefirstgenerationoftheCambridgeKeynesianswere
Keynes’directdisciplesandlearnedfromhim,notjustspecific
theories,butacertainstyleofeconomicreasoningandexpression.In
thispaper,IdiscusstheextenttowhichHarrodconformstothe
characteristicsoftheCambridgeKeynesiansasidentifiedbyPasinetti,
andfindthat,byandlarge,hewasinagreementwiththem.Andyet
despitetheircommonrootsinKeynesandtheirsharedadherenceto
hisgeneralapproach,Ifindthatonanumberfundamentaltheoretical
issuesthereweresharpdifferences.Thefirstrelatestothe
assumptionofalong‐runfullemploymentequilibriumin
macroeconomics.TheassumptionhasnoplaceinHarrod’sthinking
butiscentraltotheCambridgeKeynesiandistributiontheory.The
secondissuehastodowithappropriatetheoryfortherateofprofit.
Employingthefullemploymentequilibriumassumptionanda
conceptoftheaggregatequantityofcapital,theCambridge
Keynesiansdevelopedanequationthathastherateofprofitdepend
onlyonthenaturalrateofgrowthandtherateofsavingoutofprofit.
Harrod,ontheotherhand,heldthatKeynes’liquiditypreference
theoryofinterest,togetherwiththeconceptofthemarginalefficiency
ofcapital,obviatestheneedforaseparatetheoryoftherateofprofit
thatreliesonanaggregatemeasureofcapital.Finally,thethirdissue
hastodowithamisunderstandingonthepartofHarrod’sCambridge
criticsofthemethodologicalstatusofhisfundamentalequations,
leadingthemtorejectthewarrantedrateofgrowthasanunrealistic
representationofthepathoftheeconomythroughtime.Iargue
Harrodispartlytoblameforthismisinterpretationbecausehelefthis
theoryincomplete,lackingthemorecompleteeconometricmodelthat
hehadenvisioned.
____________________________________________________________
Forpresentationat40YearsoftheCambridgeJournalof
Economics,McGrathCentre,StCatharine’sCollege.July12‐13,2016.
Preliminarydraft:commentswelcome.
1
1. Introduction OnecouldreasonablyexpectHarrodandtheCambridgeKeynesianstohavemuchin
common.TheoriginalcoreoftheCambridgeKeynesiansoverlapwiththemembers
oftheCircus,1agroupofyoungeconomistswhohelpedKeynesrefinehisideasashe
movedfromtheTreatisetotheGeneralTheory.Harrodwascloseinagetothe
membersoftheCircusandhadspentaterminCambridgeasastudentofKeynesin
1922.Insubsequentyearshecorrespondedfrequentlywithhimonmattersof
economictheoryandlikethemembersoftheCircus,wasexcitedaboutcontributing
tohisrevolutionaryeconomics.ButHarrodwasinOxfordandnotpartofthe
intensediscussionsamongtheyoungeconomistsinCambridgethatcontinuedinthe
so‐called“secretseminar”inKahn’sroomsatKing’sCollegeformanydecades.
Inhisaddresstotheconferencecommemoratingthe25thanniversaryofthe
CambridgeJournalofEconomics,LuigiPasinetti(2005)surveystheprogressofthe
CambridgeKeynesianssincethe1930s.Thesamethemewasdevelopedmorefully
inhis2007bookKeynesandtheCambridgeKeynesians,subtitledA“Revolutionin
Economics”tobeAccomplished(Pasinetti2007).Hisdiscussionrevolvesarounda
numberoffeaturesthatheclaimscharacterizetheCambridgeKeynesians.
Reviewingtheninefeatures2identifiedbyPasinetti,oneishardpressedtofindany
thatHarrodwouldfindobjectionable.Andyet,Harrod’ssubstantivecontributionsto
economicswereneverfullyembracedbyhiscolleaguesinCambridge.Hisgreatest
achievement,thespecificationofhisfundamentalequationsfordynamiceconomics,
wasrecognizedasagoodstartingpoint,butbothJoanRobinsonandNicholas
Kaldorbelievedtheyhadfoundflawsinhisanalysis.Muchlikeneoclassicalgrowth
theorists,theCambridgeKeynesiansconcludedthatdynamiceconomicscould
proceedwithoutHarrod’snovelconceptofthe“warrantedrateofgrowth.”
Similarly,Harroddeniedaroleinhisownthinkingforwhatisarguablythecentral
theoreticalcontributionoftheCambridgeschool:theirtheoryofincome
distributionbetweenprofitsandwages,andtheassociatedtheoryoftherateof
profit.
Inthispaper,IexplorehowstartingfromasharedappreciationofKeynes’
contributionandagreeingonthevariousmethodologicalissueslistedbyPasinetti,
HarrodandtheCambridgeKeynesiansendedupwithsuchdisparatetheories.I
arguethattheCambridgeKeynesians,muchliketheneoclassicaleconomists,failed
toappreciatethemethodologicalstatusofHarrod’sfundamentalequations.
Moreover,indevelopingtheirtheoryofdistribution,theCambridgeKeynesiansare
workingwithadichotomybetweentheshort‐runandlong‐runthathasnoplacein
Harrod’staxonomy.Harrod,forhispart,canbecriticizedforprovidingonlyarough
1RichardKahn,JamesMeade,AustinRobinson,JoanRobinsonandPieroSraffa
madeuptheCircus.
2Intheoriginaladdresstherewereeightfeatures,hisbooklistsanadditionalone.
2
suggestiononhowacompletemacrodynamictheorycouldbeconstructed,leaving
roomformisinterpretation.
2. Harrod and Pasinetti’s List i)Realism
ThefirstfeatureonPasinetti’slistofcharacteristicsdefiningtheCambridge
Keynesianapproachisrealism:theideathat“reality(andnotabstract)rationalityis
thestartingpointforeconomicstheory”andthat“theoryneedstobebasedon
factualevidenceandnotonlytobeempiricallytestedattheend”(Pasinetti2007,
219–20).PasinettiisdistinguishingtheCambridgeapproachfromthethreestep
axiomatic‐deductivestrategywherebyonespecifiesassumptionswithaneyeto
mathematicaltractability,usesmathematicstodrawouttheimplicationsofthe
assumptions,andthenteststheimplicationsagainstreality.
Harrodwouldagreeontheimportanceofrealism.Throughouthiscareer,hetook
bothaphilosophicalandapracticalinterestininductionandempirical
investigation.His1938presidentialaddresstotheeconomicssectionoftheBritish
Associationwasonthescopeandmethodofeconomics.Hisruminationson
philosophicissuesculminatedinabook,FoundationsofInductiveLogic,thathe
regardedas“thegreatestofhisachievements,andhisclaimtoimmortality”(Brown
1980,29).
Inhispresidentialaddress,Harrod(1938,386)statesitspurposeisto“emphasize
thelimitationsofdeductionandtheimportanceofobservationofthefacts.”Later
hewouldcautionagainstthegrowingtrendofde‐emphasizingtherealismofthe
assumptionswhenhewrites:
Theoreticaleconomistssometimespresentalonglistofassumptionswith
theairofsomeonelayingthedinner‐table;intheirmindsthemealisto
consistinthemanipulationoftheformulaeexpressingtheassumptions.In
economicsthechoiceofappropriateassumptionsisoftenthemore
importantofthetwostages.(Harrod1956,312)
Inordertoimproveone’sjudgmentastotheselectionofassumptions,Harrod
believeditwasimportanttohavestronggroundingintheinstitutionaland
quantitativeaspectsoftheeconomy.Hewasaproponentofsurveyandfieldstudies,
takinganactivepartintheOxfordEconomists’ResearchGroup,whichconducted
systematicinterviewsofentrepreneurstoestablishfactsregardinginvestmentand
pricingdecisions(DanieleBesomi1998).
Harrod’scorrespondencewithKeynesabouthispresidentialaddressrevealsthathe
hadmoresympathythanKeynesforthenewlyburgeoningfieldofeconometrics.In
his1948lecturesondynamiceconomics,hewentasfartosay:“Iamconvincedthat
economictheorywillonlymakegoodprogresstotheextentthatitcantransform
itselfintoeconometrics”(Harrod1948,14).
3
Keynes,incontrast,washighlycriticalofTinbergen’searlyeffortsinthefield,
famouslydescribingeconometricsas“statisticalalchemy.”However,inresponseto
Harrod’sdefenseofTinbergen,Keynesconcededthateconometricswasusefulto
ascertainthemagnitudeoftheoreticalconstructslikethemultiplierandtheinterest
elasticityofinvestment.KeynesechoesHarrod’spositionwhenhewrites:“The
specialistinthemanufactureofmodelswillnotbesuccessfulunlessheisconstantly
correctinghisjudgmentbyintimateandmessyacquaintancewiththefactstowhich
hismodelhastobeapplied”(Moggridge[1973]1987b,300).
TheobjectionthatKeyneshadtoeconometricswasitspretensiontobeproviding
thequantitativeresearcherwiththepowermakeeconomicpredictionsby
furnishingnumericalestimatesoftheparametersinamodel.FromKeynes’pointof
view,econometricsisnotmuchmorethanhistoricaldescription,andany
predictionsbasedonparameterestimatesneedtoincorporatejudgmentsbasedon
one’sknowledgeofbackgroundfactorsnotincludedinthemodel,sincethevalues
oftheparametersaresusceptibletochangethroughtime.
ii)Non‐ergodicity
Modelswithchangingparametersrelatetotheideaofnon‐ergodicitythatPasinetti
includesasanothercharacteristicoftheCambridgeKeynesians.Thetermwas
popularizedbyPaulDavidson(1982)tocapturewhatKeyneswasgettingatwhen
hewrotebywayofcriticismofTinbergenthat“theeconomicenvironmentisnot
homogenousoveraperiodoftime”(ibid.,189n.6).Davidson’spositionisthatnon‐
ergodicityinvalidatestherationalexpectationsresearchprogram,sincepastdata
cannotbeusedtoforecastthefuture.
Non‐ergodicityalsorelatestothedistinctionmadebyJoanRobinsonandothers
betweenlogicalandhistoricaltime.Ifoneacceptsthattheeconomicsystemevolves
overtimeinanessentiallyunpredictableway,thescientificpretentionsofmuch
econometricworkareunjustified.AlthoughHarrodwasenthusiasticabout
econometricsinprinciple,hedidnotfollowthroughinacompleteeconometric
specificationofhistheory,soitisuncertainhowhewouldhavedealtwiththeissue
ofnon‐ergodicity.
iii)Causality
Pasinetti(2007,226)notesthat“thequestionofhistoricaltimeopensupthenotion
ofcausality.”Herecognizesthatifoneisworkingwithasystemofsimultaneous
equations,asiscommonwithinmainstreameconomics,therelativeimportanceof
causesisnotimportant.Theproblemheseeswithamodelmadeupofasystemof
equationsinwhichvariablesaremutuallydeterminedisthe“unjustifiedsharp
distinctionwhichconsidersanyspecificvariableaseithertotallyunimportant(and
inthiscasetobeneglected)orofsomeimportanceandinthiscasetobeconsidered
exactlyonthesamelevelas,andsymmetricallyto,anyoneoftheothervariables”
(ibid.).
4
RelativetotheCambridgeKeynesians,Harrodwassomewhatlesscriticalofthe
simultaneousequationmodelthatmakesupmainstreamgeneralequilibrium
theory.Thismayinpartbeexplainedbyamoreconservativetemperament
reluctanttothrowawaypastachievements.HarrodbelievedKeyneswasinclinedto
overstatetherevolutionarynatureofhiscontribution,remarkingthat“thismay
havedonesomeharmtotheprogressofeconomictheory,whichshouldconsistofa
systemofharmoniousconcepts”(1973,63‐4).
Insteadofabandoningearliertheories,Harrodproposedthateconomictheorybe
dividedintofourcompartments.Firsttherewasthedivisionbetween
microeconomicsandmacroeconomics,andtheneachofthosecouldbedividedinto
staticsanddynamics.Accordingtothisscheme,theneoclassicaltheoryofvalueand
distributionintheformofasystemofsimultaneousequationscouldbepartitioned
intomicroeconomicstatics,quiteapartfromhismacroeconomicdynamics.Hewas
satisfiedthatthemodelcouldstayaslongasitdidnotpretendtobeabletodeal
withtopicsbettercoveredintheothercompartments.
Butwhileacceptingaplaceforageneralequilibriummodelwithineconomics,
Harrodwasconsciousandwaryofatrendtowardsexcessiveformalizationofthe
model.Hewritesof“theerodingprocess,tendingtonarrowdownstaticeconomics,
takingthelifeoutofitanddepartingwidelyfromtheintentionsofitsauthors”
(Harrod1948,6).Harrodlikenedmodelstomaps:“asimultaneouschartorsurvey
oftheeconomicfield,andthemainworkofthecartographerisanalysisand
classification”(Harrod1938,387).Herecognizedthattheworkoftheeconomistis
notdonesimplybysettingoutanabstractmodel.Themodelratherservesasa
guidetoaidtheinvestigatorinprovidingacompletecausalexplanationofthe
phenomenaunderconsideration.
iv)Internalconsistency
Harrod’sstressontheimportanceof“maps”toguideourthinkingrelatestoanother
itemonPasinetti’slist:theimporanceofeconomiclogicwithinternalconsistency.
TheimpetusforHarrod’sdynamicmodelwas,infact,thelogicalinconsistencythat
hedetectedinstaticmodels,includingKeynes’,withpositivesavingandinvestment.
Ifcapitalisaccumulatingonecannottakeitslevelaspartoftheceterisparibus
backgroundofthetheory,andhencetheneedforaradicallydifferenttypeoftheory.
Harrod(1939,15)claimed“anewmethodofapproach—indeedamental
revolution—isneeded”todealwiththegrowthofeconomicoutputandcapital,ina
logicallyconsistentway.
v)Macrobeforemicro
Harrod’smentalrevolutionsoughttobringbackwhatBaumol(1970)hascalledthe
MagnificentDynamicsoftheclassicaleconomistslikeRicardoandJamesMill.Here
againHarrodfindshimselfonthesamegroundastheCambridgeKeynesians.
Pasinettinotesanotherofthedistinctivefeaturesoftheschoolistheirputting
macroeconomicsaheadofmicroeconomics.Analternativewayofframingthis
5
featureistosaytheyrejectthenotionthatmacroecomicsneedstobegroundedin
neoclassicalmicroeconomics.
Asnotedabove,Harrodthoughtofmicroeconomicsandmacroeconomicsasexisting
independentlyofoneanotherinseparatecompartments.ForHarrod,aspectsof
Keynes’theoryproperlybelongwithinmacroeconomicdynamicsandifviewed
throughthelensoftraditionalmicroeconomimcs,itwouldbemisunderstood.For
instance,Harrod(1973,65)writes: “Somecommentatorshavesuggestedthat
Keynes’systemdependsonwagesbeingflexibledownwards,asindeedtheyusually
arethesedays.Thisshowsacompletelackofintellectualgraspofhissystem.”
vi)Malthusforinspiration
Relatedtotheideaoftheprimacyofmacroeconomicsistheinspirationthatthe
CambridgeKeynesianstakefromMalthus.ForKeynes,thepartsofMalthus’s
economicsthathefoundmostattractivewerehisideasaboutunderconsumption
creatinganinsufficiencyofaggregatedemand.Amongeconomiststrainedtothink
ingeneralequilibriumtermstheso‐calledparadoxofsavingwasconsidereda
fallacythatonlythosewithoutpropereducationineconomicswouldembrace.
Keynes,however,sidedwiththe”braveheretics”likeJ.A.Hobson,whofollowed
Malthusincontinuingtoarguethatsavingwouldnotalwayspropeltheeconomy
forward.JoanRobinson(1949,80)recognizedtheimportanceofHarrod’sworkfor
thedevelopmentofMalthus’sinsights,remarkingthatHarrod’sdynamicanalysis
representsthe“missinglink”betweenKeynesandHobson.
vii)Appropriateanalyticalframework
PasinettistressestheimportancefortheCambridgeKeynesiansofgoingbeyond
criticismofmainstreameconomicsanddevelopinganalternativeframework.
Harrodbelievedthatinsettingouthisfundamentalequationshewascontributing
tosuchaframework.HethoughtKeyneshadnotfullyescapedfromastaticanalysis,
andthathistheoryneededtoberecastindynamicform.Inthesimplestform,
ignoringinternationaltrade,Harrod’sfundamentalequationsrelatetherateof
growthinoutput,∆Y/YorG,totheaveragepropensitytosave,S/Yors,andthe
incrementalcapital‐outputratio,I/∆YorC,suchthat
s
G
(1)
C
Expressedas,
S
Y
 Y I
Y
Y
(2)
6
oneseesthattheequationisequivalenttotheaccountingidentityS=I.Indeed
Harrodsumsuphismodelasthedynamisedversionofthesavinginvestment
identity.
Harrodunderstoodthathisequationwasatautologyandnotsusceptibleto
refutation.Butitwasthebasisforhismap‐‐hissystemofclassificationinwhichhe
presentshisdefinitionsoftheactual,warrantedandnaturalratesofgrowth.The
actualrateofgrowthissimplythatratethatoneobservesatapointoftime.The
warrantedrateisahypotheticalratethatwouldbeachievedifpeopleweresaving
attheirdesiredlevelsandproducerswerecontentwiththeamountofinvestment
theywerecarryingout;itisanequilibriumratebutnotnecessarilyonethatbrings
alongfullemploymentofresources.Thenaturalrateofgrowthrepresentsthe
highestrateofgrowththatispossiblegiventhegrowthofthelaborforceandof
technicalknowledge.
TheusetowhichHarrodputshismodelisintheanalysisofdivergencesbetween
theactual,warrantedandnaturalratesofgrowth.ThedangerthatHobsonand
Malthuspointedtoresultsfromasituationinwhichthewarrantedrateisabovethe
naturalrate.
Ifthewarrantedrateisabovethenaturalrate,theactualratemustbebelow
thewarrantedrateformostofthetime,andthecentrifugalforcespullit
furtherdown,causingfrequentperiodsofunemployment.(Thisisthe
dynamisedversionofthestagnationthesis.)(Harrod1959,455)
viii)Instability
Harrod’sequationforthewarrantedrateallowsonetoseehowevenasmall
exogenouschangeingrowthcangenerateinstability.Ifthegrowthrateweretorise
abovethewarrantedrate,ahigherlevelofinvestmentwouldbenecessary.Ahigher
levelofinvestmentwouldcausethegrowthratetoriseevenmorethroughthe
operationofthemultiplier,pushingtheeconomyfurtherfromequilibrium.
Similarly,ifthegrowthrateweretofallbelowthewarrantedrate,entrepreneurs
wouldbemorepronetoscalebacktheirinvestmentplans,creatingacontractionary
effect.Harrodcalledthesetendenciescentrifugalforces.
Solow(1956,65)usedtheterm“knifeedge”todescribetheinstabilityinHarrod’s
modelbutHarrodwasunhappywiththisinterpretationandtookpainstosetthe
recordstraight:“So,onceagain,Imustprotestagainstadescriptionwhichgivesan
entirelyfalseimpressionofmyviews.…Ihopethatweshallhearnomoreofthe
‘Harrodknife‐edge’”(Harrod1970,741);andthenafewyearslater,“Ihaveto
protestagainsttheknife‐edgenomenclature,becauseitsoundstotallyunrealistic
andevenatrifleridiculous,andmightdistractthereader’smindfromgivingserious
attentiontowhatIhavetosayaboutinstability”(Harrod1973,33).
7
Harrod’sobjectiontothetermwasthesuggestionthatevenasmalldeviationsfrom
theequilibriumwouldleadtoaviolentmovementawayfromthewarrantedrateof
growth.Heimaginedthemovementtobemuchmoregradualandpronetoallkinds
offrictions,morelikethetopofaflatdomethanaknifeedge:“theamountoffriction
dependsonbuilt‐inprocedures,degreeofconservatism,sensitivitytocurrent
changesday‐by‐day,uncertaintiesaboutthefuture,sensitivitytochangesof
expectations,thekindofphenomenathataffectexpectations,etc.Itneedsempirical
study,ratherthantheory,toevaluatetheamountoffriction”(Harrod1970,740).
ix)Socialconcern
Theperceivedinstabilityofanunregulatedeconomicsystembringsustothefinal
itemonPasinetti’slistofthecharacteristicsoftheCambridgeKeynesians.Itisa
deeplyfeltsocialconcernarisingfromtheirbeliefthatthefreemarketcannotbe
reliedupontobringaboutprosperityandwell‐being,thateconomicpoliciesare
necessarytoimproveeconomicoutcomes.Onthispoint,aswellastheothers
discussedabove,thereisnotmuchdifferencebetweenHarrodandtheCambridge
Keynesians.Temperamentally,Harrodwasmoreconservative,whichshowsupin
hiswishtopreservetheneoclassicaltheoryofvalueinaseparatecompartmentof
microeconomicstatics,aswellasinsomeofhispoliticalopinions.Butasfaras
constructiveeconomictheorygoes,HarrodandtheCambridgeKeynesiansare
agreedonthenecessityofasteppingoutsideageneralequilibriumframeworkand
developingarealisticcausalmacrodynamicsthatrecognizestheproblemsof
underconsumptionandtheinherentinstabilityofmoderneconomies.
Andyet,despiteallthesecommonalities,fundamentaldifferencesintheir
theoreticalcontributionsareevident.MostimportantlytheCambridgeKeynesians
werecriticalofHarrod’sconceptofthewarrantedrateofgrowth,anddeniedita
placeintheirschema.
8
3. Criticisms of Harrod AsDanieleBesomi(1999,198–215)documents,Harrod’sworkoneconomic
dynamicshasbeenwidelymisinterpreted.Harrodhassufferedthefateofbeing
frequentlycited(usuallyinconjunctionwithDomar)butrarelyreadintheoriginal.
Inthe1960sandbeyond,adistortionofhisoriginalintentwascodifiedin
macroeconomicstextbooks3withinthechapterscoveringlongrungrowththeory,
wherethethreefundamentalequationswerecollapsedintoone,andtakento
representalong‐rungrowthpath.Theprevailingideawasthatinthelong‐run,
resourcesarefullyemployed,soonlyHarrod’sequationforthenaturalrateof
growthneedstobeconsidered.
TheneoclassicalcritiqueofHarrod’sconceptofthewarrantedrateofgrowthwith
unemploymentisthatfactorpriceswilladjusttoinsurefullemploymentoflabor.If
workersareunemployed,thewageratewillfallrelativetotheinterestrate,and
leadfirmstosubstitutelaborforcapital.Solow(1994,47)writes:
Thestandardneoclassicalmodel,ofcourse,resolvestheproblembymaking
theoutput‐capitalratiotheendogenousvariable.…Itfitswellwiththerestof
economics;thepossibilityofincreasingtheoutput‐capitalratioby
substitutinglaborforcapitalisacomfortableandsensibledevice,especially
onalongishtimescale.Theimpliedadjustmentmechanismisplausibleand
familiar.…Theassumptionsaboutdiminishingreturnsthatarerequiredto
makethismechanismworkcomeeasilytomosteconomists.Substitution
alongisoquantsisroutinestuff.
Butevenattheleveloftaxonomy,Harrod’svisionisviolated,when
macroeconomicsisdividedintoshort‐runbusinesscycletheoryandlong‐run
growththeory.Asdiscussedabove,Harrodbelievedtheappropriateclassification
formacroeconomicswasintostaticsanddynamics.Hisoriginalinterestwasinthe
areaofshort‐runfluctuations,andthedebatebetweenHayekandKeynes(Harrod
1959,451).Hisinsightwasthattodisentangletheconfusionsinthecontroversy,it
wasnecessarytomovebeyondastaticanalysis.Henotesthatinthediscussionsof
thecycle,theoriststend“toregardthephenomenaoftheirstudyintermsof
transitionsfromonestaticequilibriumtoanother.”Hecontinues:
Itmaybethattheywouldbegreatlyassistediftheycouldregardthemas
departuresfromoroscillationsaboutapathofgrowth;buttheycanonlydo
thiseffectivelyifthelawsgoverningincreaseareaspreciselyformulatedas
thestaticlaws.Weneedasystemoffundamentalequationsusing
simplifyingassumptions—cf.thefrictionlesssurface,etc.—inwhichratesof
increasewillthemselvesfigureasunknownterms.(Harrod1938,403)
3Harrod’smodelisgraduallydisappearingfromthetextbooksasthedynamic
generalequilibriumapproachengulfsthediscipline.Butitoccasionallymakesare‐
appearance,indistortedform,inotherplaces;e.g.,Piketty(2014,230–31).
9
Harrod’sideaforthefundamentalequationswastocapturetheforcesactingona
growingsystem,atapointintime,inordertobetterunderstandshort‐run
fluctuations.Heusedtheanalogyofatraintravelingdownthetrackataconstant
velocity,versusonemovingfromastationaryposition(Harrod1934,478).Theset
offorcesactingonthetrainwhileitisinmotionaredifferentfromthosewhenitis
atrest.Andyetonecanstillconsiderthoseforcesatapointintime.
Theneoclassicaldivisionofmacroeconomicsintolong‐runandshort‐runanalysesis
alsoevidentintheworkoftheCambridgeKeynesians.Inaseminalarticleinwhich
hegivescredittoJoanRobinsonforworkingoutsimilarideas,Kaldor(1955,94–95)
dividesmacroeconomicsintothetwostandardcompartments:short‐runstatic
theoryinwhichaggregatedemandisaconsiderationindeterminingoutput,and
long‐rundynamictheoryinwhichoutputisgrowingatthenaturalrate(determined
bythegrowthinpopulationandtechnology.)Byassumingfull‐employment,
Kaldor’sKeynesiandistributiontheorymakesaradicaldeparturefromHarrod’s
model.
BothKaldorandHarrodregardedKeynes’analysisintheGeneralTheoryas
incompleteandattemptedtoextenditintothe“long‐run.”Butwhereas,Kaldor
conceivedthelong‐runasastateoffullemployment,forHarroditonlymeantthat
capitalwasaccumulating.
KaldoremploysKalecki’sideaofdecomposingoutputintowagesandprofitssothat
thesavingsinvestmentidentitybecomes:
(3)
s p P  s wW  I wherewherespistheaveragepropensitytosaveoutofprofitsP,swistheaverage
propensitytosaveoutofwagesW,andIisthelevelofinvestment.IsolatingPon
oneside,anddividingbyagivenlevelofoutputleadstotheconclusion,thatthe
profitshareisdeterminedbytherateofinvestmentrelativetooutputandthe
propensitytosaveoutofwagesandprofit.
(4)
TheweaknessinKaldor’smodel,however,isitsrelianceontheassumptionofan
exogenouslygivenlevelofoutput.Ifoutputisvariable,thentheequationamounts
tonothingmorethananalgebraicrearrangementofanaccountingidentity.Butif
outputisgiven,theequationcannotbeusedtoanalyzeKeynesianproblemsof
unemploymentandinsufficientaggregatedemand,orbeusedtocriticizeHarrod’s
conceptofthewarrantedrateofgrowth.4
4
ProblemswithKaldor’sdistributiontheorydidnotescapethenoticeofRobert
SolowwhowrotetoFrankHahnin1959:“Nicky’smodelsimplywillnotstandup
10
Nevertheless,Kaldorproceedstoreasonthatinthelong‐run,undertheconditionof
fullemployment,anincreaseininvestmentmustresultinhigherpricesandprofit
margins,whileadecreaseininvestmentmustresultinlowerpricesandprofit
margins.
Hencethe"warranted"andthe"natural"ratesofgrowtharenot
independentofoneanother;ifprofitmarginsareflexible,theformerwill
adjustitselftothelatterthroughaconsequentialchangeinP/Y[profit
dividedbyoutput].
Thisdoesnotmeanthattherewillbeaninherenttendencytoasmoothrate
ofgrowthinacapitalisteconomy,onlythatthecausesofcyclicalmovements
lieelsewhere‐notinthelackofanadjustmentmechanismbetweens[the
averagerateofsaving]andGv[therateofgrowthmultipliedbythecapital‐
outputratio].(ibid.,97)
Similarly,JoanRobinson(1956)makesthecasethatifcertainconditionsare
fulfilled(neutraltechnicalprogress,aconstantsavingsratio,atolerablerateofreal
wagesandasituationoftranquility),afullemploymentrateofgrowthshouldarise.
AmajorpartofhercriticismwasthatHarroddidnotproperlyaccountforthe
endogenityoftheincrementalcapital‐outputratio.Ironically,Robinson’s
conclusionisthesameasthatreachedbytheneoclassicaleconomistswithwhom
shearguedsofiercelyonotherissuesrelatedtocapital.Thepaththatshetravelsto
reachit,however,isslightlydifferent.Robinson(ibid.,vii)relatesherobjectionto
theideaofawarrantedrateatlessthanfullemploymenttowhat“Hayekcalledthe
‘Ricardoeffect’—therelationofrealwagestothemostprofitable‘lengthofthe
periodofproduction.’”Theideawasthatastheeconomygrows,therealwage
increaseswhichaffectsboththeaveragepropensitytosaveandtheoptimalmixof
laborandcapital.Thechangeintherealwageaffectsthedemandforcapitalgoods
throughitsinfluenceontheircostofproduction.Robinson(ibid.,406)isledto
concludethatinequilibrium“theactualrateofgrowthandthenaturalrateof
growthareequaltoeachother,andthewarrantedrateofgrowthhas
accommodateditselftothem.”
RobinsonlaterretractedtheargumentpresentedinTheAccumulationofCapital
againstHarrod’swarrantedrateofgrowthandpresentedanotherlineofargument.
InherEssaysonEconomicGrowthshewrites:
Harrodnotonlytakestheshareofsavinginincomeasgivenbutalso
postulatesthattherateofprofitissomehowsettledinadvance;withagiven
spectrumofpossibletechniques,therateofprofitdeterminesthe
capital/incomeratio.ThusforHarrod,s/visdeterminedindependentlyofg.
underscrutiny.Whenitisnotself‐contradictoryitismoreorlesscompletely
arbitrary”(quotedinBackhouse2014,262).
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Thereisthenonlyonevalueofg(the'warrantedrateofgrowth')thatis
compatiblewithequilibrium.Whentheactualrateofgrowthislessthanthis
'warranted'rate,therealisedrateofprofitisbelowthepostulated
equilibriumlevel,whichpushestheactualratestilllower.Viceversawhen
theactualrateisabovethe'warranted'rate.Thisknife‐edgeiscreatedbythe
postulatethattheequilibriumrateofprofitisdeterminedindependentlyof
therateofgrowth.(Robinson1962,12n)
TheproblemwithHarrod’scentralideaofthewarrantedrateidentifiedbybothhis
neoclassicalandCambridgecriticswashissupposedassumptionoffixed
parametersforthecapital‐outputratio(v)5andtheaveragesavingrate(s).Their
mistake,however,wastheirfailuretorecognizethattheequationsapplytoa
hypotheticalpointintime,inwhichitmakessensetotakethemasgiven.Rather
theythoughtHarrod’sequationsweremappingaprocessofgrowththroughtime.
Heprotestedagainstthecriticismthatheassumedfixedparametersonanumberof
occasionsbutbecauseofafailuretoappreciatehisframework,hisprotestswere
ignored.
Theinterpretationofhistheorythathashiswarrantedrateofgrowthrateresting
ona“knifeedge”alsoderivesfromtheideaofconstantparametersthroughtime.
Forinstance,Baumol(1970,54‐5)soughttoridthetheoryoftheknife‐edgeby
replacingwhathetooktobeanunrealisticassumptionaboutentrepreneurial
behavior.Thesupposedassumptionwasthatentrepreneurswouldactsoastokeep
thecapital‐outputratioconstantthroughtime,sothatwitheverychangeintherate
ofgrowthofoutputtherewouldbeanimmediatereactionbyentrepreneursto
changetheirrateofinvestment.Harrod,however,nevergaveanyindicationthathe
believedentrepreneurswouldbehaveinsuchamechanicalfashionandattempted
tosettherecordstraight:
Ihavesuggestedthat,despiteacontinuingexperiencedshortageofcapital,
fixedand/orcirculating,entrepreneursmayabatetheirrateofordering,
becausetheyregardthecurrenttempoofadvanceofdemandfortheir
productsasabnormalandnotcapableofbeingsustainedindefinitely.ButI
suggestthatitwouldbepushingthisargumentmuchtoofartoregarditas
obviatingtheinstabilityprinciple.(Harrod1959,464)
MuchlikePasinetti(2007,275)withhisseparationtheorem,Harrodismakinga
distinctionbetweenhismodel,andhisinterpretationoftherealworld.InHarrod’s
analysisakeyingredienttobeleavenedwithhisequationsisjudgmentbasedon
observedempiricalregularities.Hisinterpreterstendedtomisstheroleof
empiricaljudgmentinhismethod,seemingtobelievethattheequations
incorporatedalltheempiricaljudgmentsthatHarrodthoughtshouldbemade.
5Harrodactuallyneverusedv,thecapital‐outputratio,asaparameter.The
parameterinhisequations,representedbyC,wasthechangeincapitalrelativeto
thechangeinoutput,i.e.,theincrementalcapital‐outputratio.
12
Whiletheneoclassicalcriticsplacedtheirfocusontheincrementalcapital‐output
ratio,theCambridgeKeynesiansstressedthesupposedconstancyofaverage
propensitytosave.TheyadoptedKalecki’sinsightthatthepropensitytosavewill
betypicallyhigherforcapitaliststhanforworkers,sothatachangeindistribution
wouldchangetheaverage.TheyarguedthatHarrodwasincorrecttoascribe
instabilitytothewarrantedrateofgrowthbecauseasincomeandtheprofitshare
increases,theaveragepropensitytosaveincreasesreducingtheexpansionary
effect;similarlyadecreaseinincomewouldleadtolesssavingoutofincome,thus
limitingthecontractionaryeffect.Harrodfelttheneedtoprotest:
Thereisallthedifferenceintheworldbetweenexpressingtheamountthat
peopledesiretosaveasafractionofincomeandaffirmingthattheydesireto
saveaconstantfractionofincome.Thebasicgrowthequationsarerigidand
precise,anditwouldbea“howler”tointroduceintothemasloppy
generalizationaboutwhatdeterminesthedesiresofpeopletosave.(Harrod
1973,170–71)
Alongthesamelines,whenRobinsonpointstotheeffectoftherateofprofitonthe
desiredincrementalcapital‐outputratio(Cr),Harrod(1970,738)writesinhis
defense:“Asthe‘model’hadthevirtueofgreatsimplicity,itseemedtobedesirable
topinpointit,andnottoreverttoanelaborateanalysisoftheconjugationofvarious
possibleprofitshareswithalternativegrowthpaths.”Themisunderstanding,again,
wasoneofhiscriticsexpectingmorefromhisequationsthanheintended.Harrod
(1963,404)concededthat“itisproper,ofcourse,totakebothsandCrtobeflexible
inrelationtotherateofinterest,”adding“thedifficultyistodiscoverthecorrect
theoryofinterest.”
4. The Theory of Interest and Profit TheareaineconomicsinwhichHarrodandtheCambridgeKeynesiansdivergemost
distinctlyisthetheoryregardingthedistributionofincomeamongfactorsof
production.Inhisseminalarticle,Kaldor’s(1955)claimsthatKeynesdidnothavea
theoryofdistributionandseekstofillthegap.Hedevelopsatheoryofthedivision
ofoutputbetweenwagesandprofits,andatheoryoftherateofprofitoncapital,
thatiscentraltothepost‐Keynesianresearchprogram(EichnerandKregel1975,
1295).
Surprisingly,Sraffa’s(1960)model,whichalsoplaysanimportantroleinthe
economicsoftheCambridgeschool,requiresthatoneofthedistributionalvariables
betakenasgivenfromtheoutside.Sraffa’s(ibid.,33)judgmentwasthatoneshould
considertherateofprofittobedetermined“outsidethesystemofproduction”by
themoneyrateofinterest.Inthisjudgment,hewasinlinewithKeynes,butnot
withthepost‐Keynesians.
Keynesarguedthattherateofinterestonmoney,determinedbyliquidity
preferenceinrelationtothesupplyofmoney,“rulestheroost”andthatinvestment
isadjustedsothatthemarginalefficiencyofcapital(MEC)comesintoequalitywith
13
it.TheMECistheclosestthingtoarateofprofittobefoundinKeynes’analysis.He
definesitas“therateofdiscountwhichwouldmakethepresentvalueoftheseries
ofannuitiesgivenbythereturnsexpectedfromthecapital‐assetduringitslifejust
equaltoitssupplyprice”(Keynes[1936]1964,135).Keynesremarkedin
correspondencethat“thediscoveryofthedefinitionofthemarginalefficiencyof
capital…inmyownprogressofthought…wasabsolutelyvital”(Moggridge1987a,
549).Thebeautyoftheformulationisthatisdoesnotinvolveanyaggregate
measureofcapital,whichherecognizedasimpossibletodefineinanypreciseway.
Keynes(ibid.,p.36)heldtheviewthat“ourprecisionwillbemockprecisionifwe
attempttousepartlyvagueandnon‐quantitativeconceptsasthebasisofa
quantitativeanalysis.”
HarrodsharedKeynesaversiontoemployingameasureofthetotalstockofcapital
inhisbasicmodel.IncontrastinghismodelwiththatofEvseyDomar,hewrites:
Ihavenevermadeanyreference,explicitorimplicit,totheamountof
outstandingcapital.Theseomissionswerenotaccidental,butdeliberateand
theresultofcarefulthoughtbeforeIcomposedmyEssay.Thesevarious
values,ofwhichItooknocognisance,will,ofcourse,havetobebroughtin
andplaytheirpartinacompletedynamictheory;theomissionsweredueto
thedesiretoachievegreatgeneralityasbefitsaveryfundamental
proposition.(Harrod1959,453)
Alongthesamelines,inhisresponsetoRobinson’sarticle“HarrodAfterTwenty‐
OneYears,”Harrodwrites:
InmybooktowhichsherefersIdeliberatelyavoidtheuseofthisconcept
[thetotalstockofcapital].Itdoesnotoccurinmyfundamentalequations.
ThatisnoreasonwhyProfessorRobinsonshouldnotuseitforthe
developmentofherowntheories,orevenforthecriticismofmine.Butwhen
shesaysthattheequilibriumgrowthrateofoutput=I/K,thisimpliesthat
theincrementalcapital‐outputratio,viz.,thatpertainingtoIinyear[sic],is
equaltotheaveragecapital‐outputratiointheeconomy.Iwouldsaythat
thisassumptionishighlyunlikelytobetrueinmostcases…Ibelievethatit
waspartlyadesiretobesafeguardedagainstsuchpitfallsthatcausedmeto
avoidtheuseoftheconceptinmybasicdynamictheorems.(Harrod1970,
739)
TheCambridgeKeynesians,incontrast,werepreparedtouseaconceptofatotal
stockofcapital(K)anddefinetherateofprofit,astotalprofitsdividedbytotal
capital.Therateofprofitinagrowingeconomyisobtainedbycombiningequation
(3)withadistortedformofHarrod’sfundamentalequationinwhichthe
incrementalcapital‐outputratio(C)isreplacedwiththecapital‐outputratio(v).By
assumingtheeconomyisonafullemploymentgrowthpath,therateofgrowth
becomesanexogenousvariable.
14
Kaldor(1955)showsthatundertheassumptionsa)thattheeconomyreachesa
long‐runequilibriumatwhichtheeconomygrowsatthenaturalrateandb)that
savingoutofwagesiszero,therateofprofitistheratioofthenaturalrateofgrowth
totheaveragepropensitytosaveoutofprofits6:
(5)
ForHarrod,however,therewasnosenseinwhichthenaturalrateisalong‐run
equilibrium.ForHarrodtheappropriateclassificationformacroeconomicswasinto
staticsanddynamics,anddynamicswasdefinedasthefieldinwhichtherateof
growthistheunknown,orendogenous,variable.Thenaturalrateofgrowthenters
theanalysisasaceilingontheactualrateofgrowth,whilethewarrantedratewas
toprovideananalogueforKeynes’staticideaofanunderemploymentequilibrium,
thatis,itwas“simplythedynamisedversionofKeynes’excessordeficiencyof
aggregatedemandinrelationtowhatisrequiredforfullemployment”(Harrod
1959,456).
RobinsonalsobrokefromHarrodandKeynesinheradoptionofthepost‐Keynesian
long‐runtheoryoftherateofprofit.ShebeganasafaithfuldiscipleofKeynes
acceptingthattheinterestratewasamonetaryphenomenonthatgovernedtherate
ofprofit(Robinson1951),butbytheendofhercareer,shehadreversedKeynes’
causationinsayingthat“overthelongruntheinterestratethatrentierscanexactis
dominatedbyprofitsthatentrepreneurscanearn,nottheotherwayaround”
(quotedinPivetti2005,81).
5. Conclusion HarrodandthefirstgenerationoftheCambridgeKeynesianssharedtheexperience
ofengagingpersonallywithKeynes.Theywerehisdisciplesandlearnedfromhim,
notjustspecifictheories,butacertainstyleofeconomicreasoningandexpression.
Pasinetti’s(2007)listofcharacteristicsoftheCambridgeKeynesianscapturesthis
distinctivestyle.
IdiscussabovetheextenttowhichHarrodconformstoeachofthecharacteristics,
andfindthat,byandlarge,hewasinagreementwiththem.Ifindthedifferences
thatdidemergeweremostlyaresultofhismoreconservative,lessconfrontational,
temperament.Harrodwishedtoconservewithinthediscipline,theneoclassical
generalequilibriummodelofanexchangeeconomy.Hissolutiontoitsinconsistency
withtheKeynesianapproachwastoquarantineitwithinaseparatecompartmentin
economictheory.Hemaintainedthattherewasnoinconsistencybecausethe
neoclassicaltheorycoveredadifferentdomain.
6Pasinetti(1962)showsthesameequationholdseveniftheaveragepropensityto
saveoutofwagesisgreaterthanzero.
15
AndyetdespitetheircommonrootsinKeynesandtheirsharedadherencetohis
generalapproach,Ifindthatonanumberfundamentaltheoreticalissuestherewere
sharpdifferencesbetweenHarrodandtheCambridgeKeynesians.Thefirstrelates
totheassumptionofalong‐runfullemploymentequilibriuminmacroeconomics.
TheassumptionhasnoplaceinHarrod’sthinkingbutiscentraltotheCambridge
Keynesiandistributiontheory.Thesecondissuehastodowithappropriatetheory
fortherateofprofit.Employingthefullemploymentequilibriumassumptionanda
conceptoftheaggregatequantityofcapital,theCambridgeKeynesiansdeveloped
anequationthathastherateofprofitdependonlyonthenaturalrateofgrowthand
therateofsavingoutofprofit.Harrod,ontheotherhand,heldthatKeynes’liquidity
preferencetheoryofinterest,togetherwiththeconceptofthemarginalefficiencyof
capital,obviatestheneedforaseparatetheoryoftherateofprofitthatreliesonan
aggregatemeasureofcapital.Finallythethirdissuehastodowitha
misunderstandingonthepartofHarrod’sCambridgecriticsofthemethodological
statusofhisfundamentalequations,leadingthemtorejectthewarrantedrateof
growthasanunrealisticrepresentationofthepathoftheeconomythroughtime.
TheassumptionofafullemploymentlevelofincomewassomethingHarrodhad
reasontothinkaboutcarefully,asitwasanissueoverwhichheandKeynesargued
fiercelyincorrespondence.Thepointofcontentionwaswhetherthe“classical”
theoryofinterestwaslogicallycoherent.Harrodarguedthatifoneassumedafull
employmentlevelofincome,thetheorymadelogicalsense—althoughheagreed
thattheassumptionoffullemploymentneededtobeabandoned,andthatthe
implicationsofdoingsoweresignificant.HesaystoKeynes:“Ithinkyouare
saying—andrightly—thattheinclusionofdependentvariabilityoflevelofincome
necessitatesradicalreconstruction”(Moggridge[1973]1987a,553).Buthe
discouragedKeynesfromdenyingtotheclassicalviewa“logicalandwater‐tight
view,albeitonewhichneglectedthemostimportantfeaturesofthesituation”(ibid.,
532).
Keynes,however,inhisstubbornrealism,couldnotevenentertaintheassumption
ofagivenlevelofincome,insistingthatitwasdependentontheothervariablesin
themodel.InlightoftheKeynes‐Harrodcorrespondenceontheclassicaltheoryof
therateinterest,itissurprisingthatKaldor(1955)beginshisKeynesianmodelof
distributionwiththeassumptionofafull‐employmentlevelofincome.Thekeyto
understandingtheapparentcontradictionistorealizethatforKaldorandhis
followers,Keynesanalysisofaggregatedemandaffectingoutputonlypertainstothe
short‐run,andaseparatetheoryappliestothelong‐run.Similarly,Keynes’theoryof
interestcouldbeconstruedasapplyingintheshort‐run,with“real”variables(the
naturalrateofgrowthandthepropensitytosaveoutofprofits)governingitinthe
long‐run.
ForHarrod,however,thelong‐runandshort‐rundistinctionplaynoroleinhis
overallschema.His1938addressonmethodologyrevealshismindsetashewas
digestingKeynes’theoryandrefininghisown.Heremarksontheimportanceof
classification,“ahighlyrespectablescientificactivityofwhicheconomistshaveno
16
needtobeashamed”(Harrod1938,392‐93).Theclassificationthathehitonfor
macroeconomicswasbetweenstatics,intowhichKeynes’modelfits,anddynamics,
inwhichthedependentvariableistherateofgrowthofoutput.
HarrodinterpretedKeynes’modelasbeingessentiallystaticsincethedependent
variablewasthelevel,andnottherateofgrowth,ofoutput;butstillherecognized
suggestionshintingatadynamicmodel.Itisthetensionbetweenthestaticand
dynamiccomponentsinKeynes’theorythathasledtointensedebatesaboutwhat
hereallymeant.Hicks’staticIS‐LMmodelbecamethestandardinterpretationofhis
theorybutPostKeynesianwriters,andeventuallyevenHicks(1980,139)himself,
arguethatmuchinKeynesislostinthisconstruction.
Itwasinthespiritofsettlingonthe“map”formacroeconomicdynamcis,that
Harrodformulatedhisfundamentalequations.Atonepointhesuggeststhathis
fundamentalequationsareanalogoustoFisher’squantitytheoryequation,MV=PT
(Harrod1948,80).Assuch,theyarenotmeanttochartthemovementofthesystem
throughtime,butrathersimplyindicatethewayinwhichthekeyvariablesmustfit
together.
IarguethatHarrod’scriticsfailedtounderstandthemethodologicalstatusofhis
fundamentalequationswhentheycriticizedhimforassumingthattheparameters
ofthesystemareconstantthroughtime.Harrodispartlytoblameforthis
misunderstandingbecausehenevercompletedthetaskoffleshingoutthemodel
withequationsthatdidchartthesystemthroughtime.Hesawpromisein
econometricsforthispurposebutnevermanagedtopullitthroughtocompletion.
InEconomicDynamicswrittenoverthreedecadesafterhisoriginalformulation,he
stressesthat“wearestillonlyonthethresholdofthesubject”(Harrod1973,vii).
ThusPasinetti’sconclusionabouttheworkoftheCambridgeKeynesians,thatthere
isarevolutionis“stilltobeaccomplished,”couldbesaidtoapplyequallyto
Harrodianmacrodynamics.
17
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